My personal guess is that it won't happen on a large scale. After all, most people feel connected to the places where they live and to the people around them. Moving to another country can be difficult if the divide (language, religion, customs, political system and its stability, law, personal and property rights, safety) is wide. This seriously limits the choice of places people would be willing to move to long-term in the first place. Historically, large-scale permanent migrations happened only if living conditions in the place of origin became hostile.
Also, where would people move to? Many destinations are developing countries and thus the cost of living there will rise in the long term. Also, these expats would be heavily affected by foreign exchange rates.
People might indeed cluster up in certain places, buy property there and live a leisurely livestyle. These factors would make prices rise and in the long term it would become less attractive to move there. This happened in Spain where property prices in premium locations have skyrocketed because of well-off people from other EU countries buying homes there. Depending on how much the goverments of the target countries care about this, they might think about countermeasures, such as restricting property acquisition to locals.
If the outflux of money becomes significant, it will affect relations with the target country as the origin country will seek to reverse the flow. Trade deals will be affected, and developmental aids, if there are any, might be reduced. If it works, the target country might make it more difficult for expats to stay long-term. But the most straightforward approach might be to limit the UBI based on residency, or make the expat lose perks such as voting rights.